Solution: Let the first polygon have 5x sides and the second polygon have 5x sides. In the second polygon, the number of sides should be 4x. Angle of an n-sided regular polygon = [(n-2)/n] radian,...
Solution: Consider that the angles of the triangle are: (a – d) o, ao and (a + d) o. We know that the sum of the angles of a triangle is 180°. Therefore, we can write: $ a-d+a+a+d=180{}^\circ $ $...
Solution: Let the first polygon have 2x sides and the second polygon have 2x sides. Let the second polygon's number of sides be x. Angle of an n-sided regular polygon = [(n-2)/n] radian, we know....
Solution: Let the angles of the triangle be (a – d) °, a° and (a + d) °. We know that, the sum of the angles of a triangle is 180°. a – d + a + a + d = 180° 3a = 180° a = 60° Given: Number of...
Solution: Let the angles of quadrilateral be given by: (a – 3d) °, (a – d) °, (a + d) ° and (a + 3d) ° This is known that the sum of angles of a quadrilateral is 360°. Therefore, we can write: $...
Solution: This is known that the sum of the interior angles of a polygon is equal to (n – 2) π, where n represents the number of sides in the given polygon. Each angle of a polygon is equal to the...
Solution: This is known that the sum of the interior angles of a polygon is equal to (n – 2) π, where n represents the number of sides in the given polygon. Each angle of a polygon is equal to the...
Solution: According to the question, one angle of a triangle measures 2x/3 grades and the other is 3x/2 degrees whereas the third angle measures πx/75 radians. We have to determine the value of x....
Solution: According to the question, 2π/5 radians is the difference between two acute angles of a given right-angled triangle. We know that π rad = 180° In terms of degrees, we can write => 1...
(vii) 125o 30’ (viii) -47o 30′ Solution: We know that 180° = π rad In terms of radians, 1° = π/ 180 rad (vii) 125° 30′ We know that, 30′ = (1/2) ° 125° 30’ = (125 1/2) ° = (251/2) o 125° 30’ =...
(v) -300o (vi) 7o 30′ Solution: We know that 180° = π rad In terms of degrees, we have => 1° = π/ 180 rad (v) -300° $ =\left( -300\text{ }\times \text{ }\pi /180 \right)\text{ }rad $ $ =-5\pi...
(iii) -56o (iv)135o Solution: We know that 180° = π rad In terms of degress => 1° = π/ 180 rad (iii) -56° Making use of the above relation, we have $ =\left( -56\text{ }\times \text{ }\pi /180...
(i) 300o (ii) 35o Solution: We know that 180° = π rad Or in terms of degrees, we can write => 1° = π/ 180 rad (i) 300° Making use of the above relation, we can write => (300 × π/180) rad =...
Solution: (v) 11c We can write the above angle in radians as => (180/ π × 11) o Putting the value of π = 22/7 $ ={{\left( 180/22\text{ }\times \text{ }7\text{ }\times \text{ }11 \right)}^{o}} $ $...
Solution: We know that π rad = 180° Or, we can write: 1 rad = 180°/ π (iii) (18π/5) Making use of the above relation, we can write => [(180/π) × (18π/5)] o Putting the value of π = 22/7 $ =\left[...
Solution: We know that π rad = 180° Or, we can write: 1 rad = 180°/ π (i) 9π/5 Using the above relation, we can write => [(180/π) × (9π/5)] o Putting the value of π = 22/7, we get $ =\left[...